"Displaying an easy familiarity with an astonishing array of primary and secondary sources, Heilbron weaves into the main story line subplots of contending egos and ideas, civic pride, aristocratic patronage and the Catholic Church's endeavors to retain cultural prestige and scientific authority in the wake of the trial of Galileo. His sensitivity to the cultural climate in which cathedral-observatories arose and operated leads him to several conclusions that many readers may find startling." - Steven J. Harris, American Scientist

"Heilbron's study is unabashedly mathematical, filled with diagrams and equations (.....) The innumerate reader will learn much from Heilbron's book, and may come away with a different appreciation of the stars above us." - Ingrid D. Rowland, The New York Review of Books

"This is not a perfect book: it is woven out of so many threads that there are some tangles in the braid; even where smooth, some readers will probably feel like they are being sneakily subjected to sections of the old math SAT." - D. Graham Burnett, The New York Times Book Review

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J.L.Heilbron's account of the use of cathedrals as solar observatories explores a fascinating chapter in the history of science.
The basic problem addressed is the measurement of time: since the earth's orbit around the sun is not neatly divisible into a whole number (of days) -- and the moon's orbit similarly is not exactly 28 days -- calendars tend to fail after a while, as the errors are compounded (seconds adding up to minutes and, over centuries, to days).
Heilbron gives an excellent overview of the fixes that have been proposed and implemented since antiquity, focussing then specifically on the efforts by the Catholic Church to fix the calendar.
The Church's unwillingness to depart from a geocentric reading of the bible added to the complexity of the problem.
A major problem faced by the Church was when to celebrate Easter -- symptomatic of the unreliability of calendars.
While measurements of the earth's orbit became increasingly exact (leading to fixes such as leap years), the precision needed to predict exactly when Easter would fall in future years had not yet been achieved by the Renaissance.
Heilbron's historical overview shows that the issues were not only scientific but also theological (the heliocentric Copernican world view seen as a challenge to the truth of the bible) and political (since the acceptance of alternate calendars could be seen as an acknowledgement of the superiority of other ideologies).
A largely forgotten chapter in history is how the Church became involved in improving the quality of observational data on which to base calendars.
Huge cathedrals were ideal solar observatories: by making a hole in the ceiling and fixing a mark on the floor where the sun's shadow fell exact measurements could be made regarding the position of the sun.
Heilbron explains both the historical and technical aspects of this very well (though perhaps in greater detail than some readers might care for).
Of particular interest are also the scientific theories applied to the data.
While the Copernican heliocentric model was not yet accepted it obviously provided a better basis for calculation.
Rather than condemning it outright, Heilbron convincingly shows that the Church allowed the model to be used for calculation -- as long as the fiction was maintained that it was a mere hypothesis, a model useful for calculation but not a reflection of reality.
Similarly, Heilbron shows the other bizarre and often byzantine means the Church dealt with science -- allowing it to flourish, in part, by deliberately ignoring it.
He also addresses the Church's process of censorship, and the consequences it had on the various players.
Heilbron's historical survey is fascinating and broad, with dozens of lively characters and some marvelous anecdotes of intrigue and discovery.
Heilbron shows that the relationship between Church and science was much more complex that is often claimed.
A rich, broad book (about a somewhat arcane subject) it is a significant addition to the history of science.
The technical detail may be challenging for many readers, but it is nevertheless a worthwhile and entertaining read.
Certainly recommended.